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Dissociation Constants of Weak Bases from Electromotive-Force Measurements of Solutions of Partially Hydrolyzed Salts

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Dissociation Constants of Weak Bases from Electromotive-Force Measurements of Solutions of Partially Hydrolyzed Salts U. S. Department of Commerce Research Paper RP2043 National Bureau of Standards Volume 43, December 1949 Part of the Journal of Research of the National Bureau of Standards Dissociation Constants of Weak Bases from Electromotive-Force Measurements of Solutions of Partially Hydrolyzed Salts By Roger G. Bates and Gladys D. Pinching A method for the determination of dissociation constants of weak electrolytes by electromotive-force measurements of solutions of partially hydrolyzed salts of a weak acid and a weak base is described. Although the precision is only half that of the conventional emf method, this procedure has particular advantage in determining t he dissociation constants of certain bases, for some of the experimental difficul ties encountered in adapting the usual method to solutions containing these bases can be overcome or red uced. The hydrogen-ion concentration of a solution of a salt of this type depends upon the constants of the weak acid, th e weak base, and water. If two of these are known, the third can be evaluated by means of e mf meas urements wi t hout the necessity of knowing the exact hydrogen-ion concentration, which is usually difficult to obtain. Hydrogen clectrodes and silver-silver chloride electrodes are used in the cells, and the solutions are aqueous mixtures containing the ions of the sa lt and an alkali chloride. The equations for t he calculation of dissociation constants are developed. The method was tested by a determination of the basic dissociation constant of tris(hydroxymethyl)aminomcthane at 20 0 , 25 0 , and 30 0 C from three se ri es of measu remen ts : (a) by t he con ventional em f method ; (b) by emf studies of the hydrolysis of mixtures of the a mine and primary potassium phosphate; and (c) by emf studies of the hydrolysis of mixtures of the amine and potassium p-phenolsulfonate. The three determinations were in acceptable agreement. The negative logarithm of the hasic dissociation constant, Pf(b, was found to be 5.946 at 20 0 , 5.920 at 25 0 , and 5.896 at 30 0 C. 1. Introduction and for the solubility of silver chloride but must Although the experimental difficulties met in the retard the diffusion of silver to the hydrogen study of most weak bases are not insurmountable, electrode as well. they have been in large part responsible for the Replacement of the silver-silver chloride elec­ failure of this important class of substances to trode by a type less susceptible to reaction with receive the attention it deserves. The hydrogen­ ammonia bases has been suggested [5, 6], but some silver chloride cell, so useful in precise determina­ sacrifice of reproducibility may be expected [7]. tions of the dissociation constants of weak acids Furthermore, it is desirable in the interest of by the electromotive-force method [1, 2, 3]1 ean consistency that dissociation constants of bases be successfully applied to a measurement of the should relate to the same cell used extensively in constant of ammonia only under special condi­ studies of weak acids and in measuring the ioniza­ tions [4]. Thus, if equimolal mixtures of ammonia tion constant of water. Nevertheless, the extra­ and ammonium chloride are to be investigated by polation to infinite dilution to obtain the thermo­ this method, one must not only determine and dynamic constant of a mono acidic base entails a apply corrections for the volatility of ammonia greater uncertainty than for a monobasic acid, where the activity-coefficient term is practically 1 Figures in brackets indicate the literature references at tbe end of tbis paper. zero, or at worst a linear function of ionic strength. Dissociation Constants of Bases 519 859368- 49--2 It is well known that the pH of an aqueous term is usually small and the extrapolation to zero solution of a salt of" two-sided weakness", that is, salt concentration is easily effected. a salt formed by neutralization of a weak acid The solutions needed to determine the dissocia­ with a weak base, is fixed by the concentration tion constant of a weak base by the emf-hydrolysis and by the dissociation constants of the acid, the method are usually not difficult to prepare. If the base, and water. These three constants are desig­ free base is a solid and is readily obtained in the nated by the symbols K a, K b , and K w, respectively. pure state, it is weighed and combined in solution Unfortunately, the pH cannot be uniquely de­ with an equivalent amount of the weak acid and termined [81. However, these dissociation con­ the desired amount of alkali chloride. If the acid stants can be expressed in terms of the measured is not a solid , and if the weak base is most con­ electromotive force of galvanic cells composed of veniently added in the form of its hydrochloride, hydrogen and silver-silver chloride electrodes im­ the solutions are made from equivalent amounts mersed in solutions of the weak salt with added of base hydrochloride and an alkali salt of the chloride. The value of KaKw /Kb can be obtained weak acid_ by a suitable extrapolation to zero concentration The chief disadvantage of this method results of salt ions. A knowledge of the hydrogen-ion from the dependence of the emf of the cell upon concentration or activity is then unnecessary. the geometric mean of two constants, that is upon The extent of hydrolysis of the salt depends upon .../Ka(Kw/K b) , instead of upon K,,/Kb alone, as in the relative magnitudes of Ka and Kw/K~. For the usual emf method. Consequently the precision best results, the acid and base should be of such of determining Kb with the aid of known values strengths that at least 5 percent of each of the of K w and Ka is reduced by one-half. two salt ions is hydrolyzed, thus assuring an Tris(hydroxymethyl)aminomethane was chosen adequate buffer capacity. Similarly, degrees of for a comparison of the new procedure with the hydrolysis greater than 95 percent should be earlier method. This primary amine can be ob­ avoided. In general, this restriction means that tained as a pure solid readily soluble in water and log Ka and log (Kw /Kb ) should differ by no not appreciably volatile. It does not react with more than 2. silver ion so extensively as to prohibit the use of the This emf-hydrolysis method is often better silver-silver chloride in equimolal mixtures of the suited to the determination of the dissociation amine and its hydrochloride. E lectromotive-force constants of weak bases than is the conventional measurements were made at 20°, 25°, and 30° C emf method. The low buffer capacity near the on solutions of partially hydrolyzed salts of this ends of the pH-neutralization curve and the amine with primary phosphate ion (H2P04 - ) and difficul ty of evaluating the buffer ratio precisely wi th p -phenolsulfonate ion (HOC6H 4SOa- ), and the in these regions usually restrict the application of dissociation constant of the base was calculated the conventional method to solutions with buffer from the results. Thc constant was also found by ratios between 0.2 and 5. Nevertheless, a low the customary emf method [1 , 3]. The three ratio of free base to salt is sometimes desired in determinations were in acceptable agreement. order to minimize losses by volatilization and II. Description of the Method errors caused by the high solubility of silver chloride in the cell solutions. If Ka for the acid If the standard potential, EO, is known, each selected is larger than K w/Kb' less than half of the emf measurement of the hydrogen-silver chloride base ion will usually be transformed into free base, cell yields a value of - log (fHjCImH), where m is and these errors may be of little or no consequence. molality, j is the activity coefficient on the molal Under these conditions the buffer ratio may depart scale. and H designates the total hydrogen-ion widely from unity, but this disadvantage is offset species, hydrated or otherwise. This quantity by the double buffering action offered by the two has been called pwH for convenience and to sug­ systems set up by the incomplete reaction of the gest its status as a practical unit of acidity sus­ salt ions with water. Furthermore, the buffer ceptible of exact definition [8]. The pwH is ratio need not be established with great accuracy. calculated from the emf E by If the free base is uncharged and the acid chosen (E-EO) F is a singly charged anion, the activity-coefficient pwH= - log (fHjClmH) = 2.3026 RT+log mCl , (1) 520 Journal of Research where F , R, and Tare respecLively Lhe faraday, base, and eq 3b will also show little tendency to gas constant, and tempera ture on the Kelvin take place. However, when both BH+ and A ~ scale. The values of E O and 2.3026 RT/F are are parL of the same aqueous system, the everal summarized in another publication [4]. Thermo­ acids and bases present interact, and hydrolysis dynamic dissociation constants are derived from is no longer dependent solely upon the acidic and experimental values of pwH by expression of mrr ba ic properties of water. For example, BH+ 01' frrmrr in terms of the constants that fix their will be hydrolyzed to a larger extent in the pres­ values in the cell solutions, and extrapolation of ence of A = than by water alone, if A = is a stronger a suitable function of the dissociation constants base than water.
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